सिद्ध कीजिये की यदि दो समरूप त्रिभुजों के क्षेत्रफल सामान हो तो दोनों त्रिभुज सर्वांगसम होते है।
Answers
दोनों त्रिभुज सर्वांगसम यदि दो समरूप त्रिभुजों के क्षेत्रफल सामान हो तो
Step-by-step explanation:
समरूप त्रिभुज
a , b , c
& d , e , f
a/d = b/e = c/f = k
=> a = dk
& b = ek
c= fk
s = (d + e + f)/2 =
Area = √s(s- d)(s - e)(s - f)
s' = (a + b + c)/2
=> s' = (dk + ek + fk)/2
=> s' = k(d + e + f)/2
=> s' = ks
Area = √s'(s'- a)(s' - b)(s' - c)
= √ks(ks- kd)(ks - kb)(ks - kc)
= √ksk(s- d)k(s - b)k(s - c)
= k²√s(s- d)(s - e)(s - f)
√s(s- d)(s - e)(s - f) = k²√s(s- d)(s - e)(s - f)
=> k² = 1
=> k = 1
a = d
b = e
c = f
दोनों त्रिभुज सर्वांगसम
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